Loading web-font TeX/Math/Italic

The Stacks project

Definition 71.18.1. With Z \subset B and f : X \to B as above.

  1. Given a quasi-coherent \mathcal{O}_ X-module \mathcal{F} the strict transform of \mathcal{F} with respect to the blowup of B in Z is the quotient \mathcal{F}' of \text{pr}_ X^*\mathcal{F} by the submodule of sections supported on |\text{pr}_{B'}^{-1}E|.

  2. The strict transform of X is the closed subspace X' \subset X \times _ B B' cut out by the quasi-coherent ideal of sections of \mathcal{O}_{X \times _ B B'} supported on |\text{pr}_{B'}^{-1}E|.


Comments (0)

There are also:

  • 2 comment(s) on Section 71.18: Strict transform

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.